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	Kronecker biography
		Kronecker was taught mathematics at Liegnitz Gymnasium by Kummer, and it was due to Kummer that Kronecker became interested in mathematics.
		Although Kronecker was not employed by the University, or any other organisation for that matter, Kummer suggested that Kronecker exercise his right to lecture at the University and this he did beginning in October 1862.
		We have already indicated that Kronecker's primary contributions were in the theory of equations and higher algebra, with his major contributions in elliptic functions, the theory of algebraic equations, and the theory of algebraic numbers.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Kronecker.html (2118 words)

	Kronecker
		Kronecker's primary contributions were in the theory of equations.
		Kronecker was taught mathematics at school by Kummer and it was due to him that Kronecker became interested in mathematics.
		Kronecker was not to become a professor until Kummer retired in 1883.
	library.wolfram.com /examples/quintic/people/Kronecker.html (374 words)

	Leopold Kronecker (via CobWeb/3.1 planetlab-4.cs.princeton.edu) (Site not responding. Last check: 2007-10-13)
		Kronecker was a student and lifelong friend of Ernst Kummer.
		Kronecker wrote 1845 his dissertation, at the University of Berlin, on number theory, giving special formulation to units in certain algebraic number fields.
		Kronecker also contributed to the concept of continuity, reconstructing the form of irrational numbers in real numbers.
	leopold-kronecker.iqnaut.net.cob-web.org:8888 (299 words)

	Leopold Kronecker Biography \| World of Mathematics
		Kronecker was born into a well-to-do family, and through inheritance and business interests, he remained independently wealthy throughout his life.
		Kronecker was extremely vocal in his views on number theory and what he perceived to be the invalidity of the use of anything other than finite numbers in number theory.
		Upon Kummer's retirement in 1883, Kronecker was appointed to the chair of mathematics in Berlin, his first official teaching position, and to the position of codirector of Berlin's mathematical seminar.
	www.bookrags.com /biography/leopold-kronecker-wom (535 words)

	Kronecker delta - Wikipedia, the free encyclopedia
		In mathematics, the Kronecker delta or Kronecker's delta, named after Leopold Kronecker (1823-1891), is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
		It is important to note that the Kronecker delta is not the result of sampling the Dirac delta function.
		The Kronecker delta is used in many areas of mathematics.
	en.wikipedia.org /wiki/Kronecker_delta (366 words)

	Kronecker.htm
		Leopold Kronecker was born to Isidor Kronecker, a successful business man, and Johanna Prausnitzer, who also came from a wealthy family.
		Kronecker believed that mathematics should deal only with finite numbers and with a finite number of operations.
		It appears that, from the early 1870s, Kronecker was opposed to the use of irrational numbers, upper and lower limits, and the Bolzano-Weierstrass theorem, because of their non-constructive nature.
	www.cse.ohio-state.edu /~brinkmei/math/Kronecker.htm (228 words)

	Biography of Kronecker
		Leopold Kronecker (1823-1891) was born on December 7, 1823, in Liegnitz, Germany.
		Kronecker was taught mathematics at the Liegnitz Gymnasium by Kummer, and it was due to him that Kronecker became interested in mathematics.
		Kronecker is quoted saying "God made the natural numbers; all else is the work of man." He felt that irrational, imaginary, and all other numbers excluding the positive integers were man's work and therefore unreliable.
	www.andrews.edu /~calkins/math/biograph/biokrone.htm (1213 words)

	Leopold Kronecker (Site not responding. Last check: 2007-10-13)
		Leopold Kronecker's parents were wealthy, his father, Isidor Kronecker, was a successful business man while his mother, Johanna Prausnitzer, also came from a wealthy family.
		Kronecker's parents employed private tutors to teach him up to the stage when he entered the Gymnasium at Liegnitz, and this tutoring gave him a very sound foundation to his education.
		Kronecker's primary contributions were in the theory of equations and higher algebra, with his major contributions in elliptic functions, the theory of algebraic equations, and the theory of algebraic numbers.
	www.ce.berkeley.edu /~rlt/ce231/asst2/Kronecker.htm (467 words)

	Leopold Kronecker - Wikipedia, the free encyclopedia
		Leopold Kronecker (December 7, 1823 - December 29, 1891) was a German mathematician and logician who argued that arithmetic and analysis must be founded on "whole numbers", saying, "God made the integers; all else is the work of man" (Bell 1986, p.
		This put Kronecker in bitter opposition to some of the mathematical extensions of Georg Cantor, Kronecker's student (cf Davis (2000)pp.
		The Kronecker delta and Kronecker product are named after Kronecker, as are the Kronecker-Weber theorem, Kronecker's theorem in number theory and Kronecker's lemma.
	en.wikipedia.org /wiki/Leopold_Kronecker (339 words)

	delta function & kronecker delta
		The delta function is a eigenfunction of x and the Kronecker delta is...
		Kronecker delta G(n-k) (usually for integer argument, not real) G=1 for n=k, =0 for n not=k.
		Also, both are used to express orthogonality, given a set of vectors, the arguments being the indices of the two vectors in question: the kronecker delta if that set is countable, the delta function if otherwise.
	www.physicsforums.com /showthread.php?t=76530 (515 words)

	Kronecker Delta -- from Wolfram MathWorld (via CobWeb/3.1 planetlab-4.cs.princeton.edu) (Site not responding. Last check: 2007-10-13)
		The simplest interpretation of the Kronecker delta is as the discrete version of the delta function defined by
		The Kronecker delta is implemented in Mathematica as
		Technically, the Kronecker delta is a tensor defined by the relationship
	mathworld.wolfram.com.cob-web.org:8888 /KroneckerDelta.html (131 words)

	PlanetMath: Kronecker's Jugendtraum
		Kronecker's Jugendtraum (Jugendtraum is German for “youthful dream”) describes a central problem in class field theory, to explicitly describe the abelian extensions of an arbitrary number field
		, in which case Kronecker's Jugendtraum has been solved by the theory of “complex multiplication” (see CM-field).
		This is version 4 of Kronecker's Jugendtraum, born on 2005-02-08, modified 2005-03-18.
	planetmath.org /encyclopedia/KroneckersJugendtraum.html (189 words)

	Kronecker Canonical Form
		In addition to Jordan blocks for finite and infinite eigenvalues, the Kronecker form contains singular blocks corresponding to minimal indices of a singular pencil (see below).
		The regular and singular structures define the Kronecker structure of a singular pencil.
		We end this introductory description by briefly pointing to the relationship between structure information of the KCF and the GUPTRI form (8.28).
	www.cs.utk.edu /~dongarra/etemplates/node309.html (344 words)

	Highbeam Encyclopedia - Search Results for Kronecker,
		Kronecker, Leopold KRONECKER, LEOPOLD [Kronecker, Leopold], 1823-91, German mathematician.
		Noted as an algebraist, he was a pioneer in the field of algebraic numbers and in formulating the
		Algorithms for sums of squares and covariance matrices using Kronecker products.
	www.encyclopedia.com /SearchResults.aspx?Q=Kronecker, (266 words)

	Kronecker Symbol -- from Wolfram MathWorld
		The Kronecker symbol is an extension of the Jacobi symbol
		The Kronecker symbol can be computed using the normal rules for the Jacobi symbol
		Dickson, L. "Kronecker's Symbol." §48 in Introduction to the Theory of Numbers.
	mathworld.wolfram.com /KroneckerSymbol.html (425 words)

	Kronecker, Leopold (1823-1891)
		He acquired a passion for number theory from Ernst Kummer, his instructor at the Liegnitz Gymnasium.
		Kronecker, who made a fortune in business before returning to his academic studies, claimed that mathematical argumentation should be based only on integers and finite procedures.
		He was one of Georg Cantor's sternest critics and refused to accept the validity of the Weierstrass function.
	www.daviddarling.info /encyclopedia/K/Kronecker.html (157 words)

	Kronecker, Leopold (1823-1891) -- from Eric Weisstein's World of Scientific Biography
		Kronecker, Leopold (1823-1891) -- from Eric Weisstein's World of Scientific Biography
		After obtaining his degree, however, Kronecker managed the estate and ran the business of his uncle following his death.
		For eight years, Kronecker produced no mathematical work.
	scienceworld.wolfram.com /biography/Kronecker.html (137 words)

	Amazon.com: kronecker (Site not responding. Last check: 2007-10-13)
		On the dimensions of controllability subspaces: A characterization via polynomial matrices and Kronecker invariants (Report) by Michael Edward Warren (Unknown Binding - 1973)
		The computation of Kronecker's canonical form of a singular pencil (Report / Applied Mathematics and Programming Division, Katholieke Universiteit Leuven) by P Van Dooren (Unknown Binding - 1977)
		Complexicty of Kronecker operations on sparse matrices with applications to the solution of Markov models (SuDoc NAS 1.26:206274) by NASA (Unknown Binding - 1997)
	www.amazon.com /s?ie=UTF8&keywords=kronecker&tag=ecomplex&index=blended&link_code=qs&page=1 (401 words)

	Macros introduce new object types
		is equivalent to adding object kronecker to the set of objects present in the document model.
		A macro definition in La)TeX has two parts; the first part declares the macro and its number of arguments; the second part specifies how instances of this macro call are to be displayed.
		Since class kronecker is a subclass of binary-operator with the same precedence as multiplication, the result is a tree with kronecker as the root and with two children, one each corresponding to [tex2html_wrap5492] and [tex2html_wrap5494].
	www.cs.cornell.edu /info/people/raman/phd-thesis/html/node27.html (813 words)

	Kronecker, Leopold - HighBeam Encyclopedia (Site not responding. Last check: 2007-10-13)
		Noted as an algebraist, he was a pioneer in the field of algebraic numbers and in formulating the relationship between the theory of numbers, the theory of equations, and elliptic functions.
		Find newspaper and magazine articles plus images and maps related to "Kronecker, Leopold" at HighBeam.
		More information is at your fingertips at HighBeam Research:
	www.encyclopedia.com /doc/1E1-kronecke.html (168 words)

	Kronicas de Kronecker (via CobWeb/3.1 planetlab-4.cs.princeton.edu) (Site not responding. Last check: 2007-10-13)
		Pelicula recomendada del dia: "nivel 13" no tiene nada que ver con este tema pero se puede juntar la pelicula con un par de vueltas de tornillo y este pequeño escrito y....
		vomitado por Kronecker a las 10:41 PM
		vomitado por Kronecker a las 11:33 PM
	kronecker.blogspot.com.cob-web.org:8888 (276 words)

	Kronecker Product (Site not responding. Last check: 2007-10-13)
		The Kronecker product notation arises in many different areas of science and engineering,
		Kronecker Product of Matrices and Applications, Wissenschaftsverlag, 1991.
		The bibliography of my thesis (entries in no particular order): in bib or in html.
	www.cs.duke.edu /~nikos/KP/home.html (147 words)

	The Mathematics Genealogy Project - Leopold Kronecker
		Click here to see the students listed in chronological order.
		According to our current on-line database, Leopold Kronecker has 10 students and 1619 descendants.
		If you have additional information or corrections regarding this mathematician, please use the update form.
	www.genealogy.ams.org /html/id.phtml?id=17982 (66 words)

	Kaufman: Topics on Kronecker sets
		We obtain three theorems about transformation of sets of multiplicity onto Kronecker sets, by means of functions of various differentiability classes.
		The same method yields an improved theorem on the union of two Kronecker sets.
		KÃ-RNER, Some results on Kronecker, Dirichlet, and Helson sets, Annales Inst.
	www.numdam.org /numdam-bin/item?id=AIF_1973__23_4_65_0 (102 words)

	kronecker.de (Site not responding. Last check: 2007-10-13)
		"Why investigate such problems, given that irrational numbers do not even exist?" (Kronecker)
		This page is dedicated to Leopold Kronecker (7 Dec 1823 Liegnitz, (now Legnica, Poland) - 29 Dec 1891 Berlin, Germany)
		and to the Kronecker Delta named after him.
	www.kronecker.de (41 words)

	MATLAB Central - Newsreader - graduation project - simulink kronecker product
		E-mail me when replies are made to this thread
		I'm in serious need of a simulink implementation of the kronecker
		For my graduation project I needed to use an S-function aswell.
	newsreader.mathworks.com /WebX?14@7.T2PaaVcxl6V.1@.eedd316 (411 words)

	Bad Astronomy and Universe Today Forum - View Profile: Kronecker
		Bad Astronomy and Universe Today Forum - View Profile: Kronecker
		If this is your first visit, be sure to check out the FAQ by clicking the link above.
		Kronecker is not a member of any public groups
	www.bautforum.com /member.php?u=6747 (91 words)

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